I have two Logistic regression models, one including manually selected (hierarchical) interaction effects between few independent variables and one model without any interaction effects. Both models give a McFadden Pseudo-$R^2$=0.7112. The model with interaction effects does show some interactions as being statistically significant with Walds test. But does the fact that both models give similar Pseudo-$R^2$ mean the interaction effects are technically not needed to explain any more variance in the dependent variable? Also, what about the case if the model without any interaction effects has higher Pseudo-$R^2$ than the model with them included? How does this overall affect my interpretation of the interaction coefficients?

$\begingroup$Remember that just because you do not have an interaction term in a non-linear model does not mean that there is no interaction effect.$\endgroup$
– Jesper HybelJan 20 at 23:07

$\begingroup$So in other words, if both models acheive same Pseudo-$R^2$, then picking the simpler (or any?) one is only good for prediction purpose but not for causal analysis?$\endgroup$
– Suraj IyerJan 20 at 23:35